Journal of Statistical Physics, Vol. 3/4, 1992. p. 827-847.
The instanton thermodynamics of a spherical model analogous to the soliton thermodynamics of one-dimensional sine-Gordon and phi^4-models is constructed. Decomposition of the system phase volume integral into a sum of contributions corresponding to the thermal fluctuations above the basic and instanton vacua is obtained and all the components of this sum are found. It appears that fluctuations above instanton vacua are Gaussian at all temperature. It is shown that the phase transition temperature in the spherical model can be found from
the Kosterlitz-Thouless criterion: in the high-temperature phase the instanton configurations become thermodynamically favorable. The obtained results are exact and are naturally formulated in terms of singularity theory.